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Percent Change Formula
Percent change measures the relative difference between an original value and a new value. It is widely used in finance to track stock returns, in retail to calculate markdowns, and in general math to measure growth or decay. For a fast calculation, use the percentage increase calculator or the percentage decrease calculator to see the percentage change between any two numbers.
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What is percent change?
Percent change tells you how much a quantity has increased or decreased relative to its starting value. Expressing change as a percentage makes it easy to compare changes across different scales.
For example, if a small business grows from 1 employee to 2, and a large corporation grows from 10,000 employees to 10,005, the corporation added more total people. However, the small business grew by 100%, while the corporation grew by just 0.05%.
The percent change formula
The standard formula for calculating percent change is:
The formula
Percent Change = ((New Value − Old Value) / Old Value) × 100
The variables
- Old Value = the starting, original, or initial quantity
- New Value = the final, modified, or current quantity
Handling Increases vs. Decreases
The sign of your final result tells you the direction of the change:
- Positive Result (+): The value has increased. (e.g., +15% means a 15% increase).
- Negative Result (-): The value has decreased. (e.g., -8% means an 8% decrease).
When writing about a decrease, you can drop the negative sign if you use the word "decrease" (e.g., write "an 8% decrease" instead of "a -8% decrease").
Worked Examples: Step-by-Step Calculations
Example 1: Calculating a Percentage Increase
A stock price rises from $80 to $96. What is the percent change?
- Identify variables: Old Value = 80, New Value = 96
- Subtract Old from New: 96 − 80 = 16 (difference)
- Divide by Old Value: 16 / 80 = 0.20
- Multiply by 100: 0.20 × 100 = 20%
- Result: A 20% increase.
Example 2: Calculating a Percentage Decrease
A shopper uses a coupon to reduce a grocery bill from $120 to $90. What is the percent change?
- Identify variables: Old Value = 120, New Value = 90
- Subtract Old from New: 90 − 120 = -30
- Divide by Old Value: -30 / 120 = -0.25
- Multiply by 100: -0.25 × 100 = -25%
- Result: A 25% decrease.
Common Percent Change Mistakes
- Dividing by the new value instead of the old value. This is the most common error. If you divide the difference by the new value, your ratio will be incorrect. Always divide by the starting (old) value.
- Swapping the order of New and Old in the subtraction. If you calculate Old − New instead of New − Old, you will get the opposite sign, indicating a decrease when there was an increase, or vice-versa.
- Ignoring the sign of the change. If a value goes down, it is important to include the negative sign in the raw calculations to keep track of the direction of the change.
Run the numbers
Explore percentage and growth calculation tools to solve real-world problems:
Frequently asked questions
Percent change measures the relative difference between an old value and a new value, expressed as a percentage of the original (old) value.
We divide by the old value because we want to see how much the quantity has changed relative to its starting point. Dividing by the new value would represent the change relative to the final state, which is not standard.
A negative percent change indicates a decrease in value from the starting point. For example, a result of -15% represents a 15% decrease.
Percent change measures relative change. Percentage points measure the simple arithmetic difference between two percentages. For example, if an interest rate rises from 10% to 12%, it is a 2 percentage point increase, but a 20% relative increase in the rate.
The percent change calculator automatically computes the change, handles both positive (increase) and negative (decrease) results, and displays the exact math steps.